@jameslo I just combined all your patches into one and they all behave like yours! I don't know what was going on earlier, perhaps a typo in [expr]? But I guess it wouldn't have been created. Now the numbers are toggling between 255 and 256 and 0 and 1.5258e-05, like your screenshots.

@jameslo The patch you provided indeed shows the bug. When clicking 44.1 the number on the bottom is 0. When clicking on 1 or 48, it's 1. But @ddw_music gave a very good explanation of why this is happening.

@jameslo for ceil. I only tried the patch of the screenshot in the first post.

On my machine, no matter how many times I switch between 1 and 44.1, I always get 0 after [expr].

I can't see anything wrong with it. The result before [expr] is 255 when using both 1 and 44.1 for the first division and the multiplication. Isn't this what should be expected?

If you want to feed your signal back to the same object, you must use a [s~]/[r~] pair, otherwise Pd will correctly complain about a DSP loop. Also, I don't see any real reason for using [fexpr~], as you only reference the current sample of the input with x1[0]. If you did something like x1[-1] to reference the last sample. it would make sense, but the way you wrote this, [expr~] with $v1 should suffice.

If I'm not mistaken, iemguts is a collection of objects and doesn't come as a signle binary, which means that you only need to set its path to Pd's search paths. If you have it in your externals directory, which in turn is in Pd's search paths, then you can load an object with the library name prepended, like this: [iemguts/oreceive].

The image you posted is a bit too small to really figure out what's going on. Both for the clickiness and reading backwards, you can check this very old but still valid tutorial http://pd-tutorial.com/english/ch03s04.html
Actually, I would suggest going through the entire tutorial and not only this section. It covers a lot of ground.

You can find information on abstractions and the dollar arguments here http://pd-tutorial.com/english/ch05.html. Go to 5.1.1.2 which is focused on abstractions.